CALA-n Quantum Library

CALA-n is a quantum library of Clifford+T-based Architecture of Layout-Aware n-bit gates. CALA-n quantum library is proposed for cost-effective quantum gates transpilation, based on the layouts and the number of n neighboring physical qubits for IBM quantum computers, where 2 <= n <= 5 qubits. All n-bit gates of CALA-n quantum library are constructed from Clifford+T gates as well as designed using the geometrical approach of the Bloch sphere, based on the visual representations of the rotational quantum operations for IBM single-qubit basis gates (X, √X, and RZ) and IBM double-qubit basis gate (CX or ECR). In other words, the Bloch sphere is utilized in the CALA-n quantum library as a geometrical design tool, through the utilization of the XY-plane (the top-view of the Bloch sphere) as illustrated below.

CALA-n quantum library has a set of cost-effective n-bit gates, including:

2-bit SWAP gate
2-bit controlled-√X gate: the controlled-V gate.
2-bit controlled-√X† gate: the controlled-V† gate.
3-bit Boolean gates: AND, NAND, OR, NOR, implication, and inhibition gates.
3-bit Fredkin gate: the controlled-SWAP (CSWAP) gate.
3-bit Miller gate: the quantum distance gate.

The cost-effectiveness of these n-bit gates of CALA-n quantum library comes from the following essential configurations as well as their symmetrical structures as demonstrated in the figure below (SP is a superposition gate {H, √X, or √X†}, and AX is an auxiliary gate for constructing various 3-bit gates of CALA-n):

All control qubits of an n-bit gate are only connected to the target qubit, without any mutual connection among them. For instance, all control qubits are connected to a target qubit using Feynman (CX) gates.
The target qubit of an n-bit gate can be replaced with any of the control qubits. For instance, the target qubit can be mapped in the middle among the control qubits, to fit the layout of an IBM quantum computer efficiently.
Based on (1) and (2), SWAP gates are no longer required to connect the non-neighboring physical qubits of an IBM quantum computer for the final transpiled n-bit gates.

Experimentally, from the above-mentioned essential configurations, the final transpiled quantum circuits constructed from n-bit gates of CALA-n quantum library always have lower quantum costs and fewer depths than those constructed from standard n-bit quantum gates, e.g., n-bit Toffoli and n-bit Fredkin gates, for IBM quantum computers.

The CALA-n is a derived quantum library from our GALA-n generic quantum library [GitHub], with the following distinctive features between them, where their utilized Clifford+T gates are: I, H, Z, T, T†, and CX.

Features	GALA-n	CALA-n
How many n qubits?	n >= 3	2 <= n <= 5
Constructed from Clifford+T gates?	Yes	Yes
Constructed from non-Clifford+T gates?	Yes	No
Utilize ancillary qubits?	No	Yes
Has symmetrical structures?	Yes	Yes
Has layout-aware architectures?	Yes	Yes
Suitable for IBM quantum layouts?	Yes	Yes

For more information about the GALA-n quantum library and our introduced Bloch sphere approach, please read our paper entitled "GALA-n: Generic Architecture of Layout-Aware n-Bit Quantum Operators for Cost-Effective Realization on IBM Quantum Computers", available at https://doi.org/10.48550/arXiv.2311.06760

For more information about the CALA-n quantum library and our developed Bloch sphere approach, please read our paper entitled "CALA-n: A Quantum Library for Realizing Cost-Effective 2-, 3-, 4-, and 5-bit Gates on IBM Quantum Computers using Bloch Sphere Approach, Clifford+T Gates, and Layouts", available at https://doi.org/10.48550/arXiv.2408.01025

Installation

Install the latest version of the CALA-n quantum library using the pip command:

pip install git+https://github.com/albayaty/cala_quantum_library@main

Instead, the CALA-n quantum library can be manually installed as stated in the following steps:

Download this repository to your computer, as a ZIP file.
Extract this file to a folder, e.g., cala_quantum_library.
Use the terminal (or the Command Prompt) to cd to the cala_quantum_library folder.
Install the setup.py file using the following command:
```
 python setup.py install
```
Or, using this command:
```
python3 -m pip install .
```

Usage

First of all, please be sure that the following prerequisite packages have been installed:

qiskit (version >= 1.0).
qiskit_aer (simulating quantum circuits locally).
qiskit_ibm_runtime (transpiling and executing quantum circuits on IBM quantum computers).
qiskit.visualization (plotting histograms, distributions, etc.).
numpy (mathematical constants and calculations).
matplotlib (drawing quantum circuits).

Next, the CALA-n quantum library consists of five callable functions as follows.

2-bit SWAP gate:
```
CALA_SWAP(as_block=False, statistics=False)
```
Where,

as_block: construct a gate as a quantum circuit or a block, its default value is False, and

statistics: print the final counts of H, RZ, and CX gates, as a final quantum cost.

The CALA_SWAP function returns the 2-bit SWAP gate of CALA-n as a quantum circuit or a block. Note that this gate has 2 target qubits.
2-bit controlled-√X and controlled-√X† gates:
```
CALA_CSX(gate="CSX", as_block=False, statistics=False)
```
Where,

gate: the name of a 2-bit controlled gate: "CSX" for the 2-bit controlled-√X (controlled-V) gate as a default, or "CSXdg" for the 2-bit controlled-√X† (controlled-V†) gate,

as_block: construct a gate as a quantum circuit or a block, its default value is False, and

statistics: print the final counts of H, RZ, and CX gates, as a final quantum cost.

The CALA_CSX function returns the 2-bit controlled gate of CALA-n as a quantum circuit or a block. Note that the target qubit is the last indexed qubit.
3-bit Boolean gates:
```
CALA_Boolean(gate="AND", as_block=False, statistics=False)
```
Where,

gate: the name of a 3-bit Boolean gate: "AND" as the default gate, "NAND", "OR", "NOR", "IMP" as the implication, or "INH" as the inhibition,

as_block: construct a gate as a quantum circuit or a block, its default value is False, and

statistics: print the final counts of H, RZ, and CX gates, as a final quantum cost.

The CALA_Boolean function returns the 3-bit Boolean gate of CALA-n as a quantum circuit or a block. Note that the target qubit is the last indexed qubit.
3-bit Fredkin gates:
```
CALA_Fredkin(as_block=False, statistics=False)
```
Where,

as_block: construct a gate as a quantum circuit or a block, its default value is False, and

statistics: print the final counts of H, RZ, and CX gates, as a final quantum cost.

The CALA_Fredkin function returns the 3-bit Fredkin gate of CALA-n as a quantum circuit or a block. Note that the target qubits are the last two indexed qubits.
3-bit Miller gates:
```
CALA_Miller(as_block=False, statistics=False)
```
Where,

as_block: construct a gate as a quantum circuit or a block, its default value is False, and

statistics: print the final counts of H, RZ, and CX gates, as a final quantum cost.

The CALA_Miller function returns the 3-bit Miller gate of CALA-n as a quantum circuit or a block. Note that this gate has 3 output qubits.

Based on the heavy-hex layout of IBM quantum computers of 127 qubits illustrated in the figure below, a developer can construct cost-effective gates of CALA-n up to 5 qubits, using the I-shape qubits' arrangement as denoted by the red box in this figure. For that, the list of indexed qubits [61, 62, 63, 72, 80, 81, 82] will be utilized in the following section to construct cost-effective 4-bit and 5-bit gates of CALA-n quantum library, and SWAP gates are never added to their final transpiled quantum circuits. Note that any I-shape of 7 qubits' arrangement can be utilized in such a layout.

Therefore, various 4-bit and 5-bit gates of CALA-n quantum library can be constructed for specific Boolean and Phase purposes, such as OR-AND-OR (as a POS structure), AND-OR-AND (as a SOP structure), AND-XOR-AND (as an ESOP structure), CNF-XOR SAT, DNF-XOR SAT, majority, implication-inhibition, inhibition-implication, quantum Boolean-based gates for Boolean oracles, quantum Phase-based gates for Phase oracles, just to name a few.

We introduce CALA-n as an open and generic quantum library for prospective quantum computing research, to develop interesting and cost-effective n-bit quantum gates, which can be easily adapted with different layouts of n neighboring physical qubits for superconducting quantum systems, e.g., IBM, Google, and Rigetti.

Examples

Initially, import the required Python and Qiskit libraries (including our cala_quantum_library):

from qiskit import *
from qiskit_aer import AerSimulator
from qiskit.visualization import *
from cala_quantum_library import *
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

Then, let's construct and use the cost-effective n-bit gates of CALA-n quantum library in different scenarios as follows. Please observe the parameter qubits=[qubits-mapping-list] in Qiskit compose() instruction, this [qubits-mapping-list] gives the freedom of where to map the target qubit of an n-bit gate of CALA-n quantum library into the layout of an IBM quantum computer, to efficiently suit such a layout without adding any SWAP gate. All the following examples utilize the list of indexed qubits [61, 62, 63, 72, 80, 81, 82], based on the I-shape shown in the figure above.

Construct the 2-bit SWAP gate as a quantum circuit with statistics:

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_SWAP(as_block=False, statistics=True), qubits=[60,61], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

⟩⟩⟩ Statistics (quantum cost) of 2-bit SWAP gate of CALA-n:
     H gates = 2
    RZ gates = 0
    CX gates = 2

Construct the 2-bit controlled-√X† gate as a quantum circuit:

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_CSX(gate="CSXdg", as_block=False, statistics=False), qubits=[60,61], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Construct the 3-bit AND gate as a quantum circuit with statistics:

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="AND", as_block=False, statistics=True), qubits=[61,62,63], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

⟩⟩⟩ Statistics (quantum cost) of 3-bit AND gate of CALA-n:
     H gates = 2
    RZ gates = 4
    CX gates = 3

Construct the 3-bit AND gate as a block without statistics:

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[61,62,63], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Construct the 3-bit AND gate as a quantum circuit, and map its target qubit in the middle between the two control qubits:

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="AND", as_block=False, statistics=False), qubits=[61,63,62], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Construct the 4-bit AND gate as a quantum circuit, and map its target qubit in the middle among the three control qubits. Note that this requires to utilize:

Two 3-bit AND gates.
Three control qubits at the indices 61, 63, and 81.
One target qubit at the index 72.
One ancilla qubit at the index 62.

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="AND", as_block=False, statistics=False), qubits=[61,63,62], inplace=True )
qc.compose( CALA_Boolean(gate="AND", as_block=False, statistics=False), qubits=[62,81,72], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Implement the previous Example (6) as blocks:

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[61,63,62], inplace=True )
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[62,81,72], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Construct the 5-bit AND gate as blocks, and map its target qubit in the middle among the four control qubits. Note that this requires to utilize:

Three 3-bit AND gates.
Four control qubits at the indices 61, 63, 80, and 82.
One target qubit at the index 72.
Two ancilla qubits at the indices 62 and 81.

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[61,63,62], inplace=True )
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[80,82,81], inplace=True )
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[62,81,72], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Construct the 3-bit Fredkin gate as a quantum circuit, where its first and second target qubits utilize the indices 63 and 62, respectively:

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Fredkin(as_block=False, statistics=False), qubits=[61,63,62], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Construct the 4-bit Fredkin gate as a quantum circuit. Note that this requires to utilize:

One 3-bit AND gate.
One 3-bit Fredkin gate.
Two control qubits at the indices 61 and 63.
First and second target qubits at the indices 81 and 72, respectively.
One ancilla qubit at the index 62.

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[61,63,62], inplace=True )
qc.compose( CALA_Fredkin(as_block=False, statistics=False), qubits=[62,81,72], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Construct the 3-bit Miller gate as a quantum circuit, and map its target qubit in the middle between the control qubits:

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Miller(as_block=False, statistics=False), qubits=[61,63,62], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Construct the 3-bit controlled-√X gate as a quantum circuit. Note that this requires to utilize:

One 3-bit AND gate.
One 2-bit controlled-√X gate.
Two control qubits at the indices 61 and 63.
One target qubit at the index 72.
One ancilla qubit at the index 62.

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[61,63,62], inplace=True )
qc.compose( CALA_CSX(gate="CSX", as_block=False, statistics=False), qubits=[62,72], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Implement an arbitrary 5-bit OR-AND-OR gate (as a POS structure) as blocks. Note that this requires to utilize:

One 3-bit AND gate.
Two 3-bit OR gates.
Four control qubits at the indices 61, 63, 80, and 82.
One target qubit at the index 72.
Two ancilla qubits at the indices 62 and 81.

num_qubits = 127
qc = QuantumCircuit(num_qubits)
qc.compose( CALA_Boolean(gate="OR", as_block=True, statistics=False), qubits=[61,63,62], inplace=True )
qc.compose( CALA_Boolean(gate="OR", as_block=True, statistics=False), qubits=[80,82,81], inplace=True )
qc.compose( CALA_Boolean(gate="AND", as_block=True, statistics=False), qubits=[62,81,72], inplace=True )
qc.draw(output='mpl', style='bw', scale=1.0, idle_wires=False, fold=-1);

Reference

In case you are utilizing our n-bit gates of CALA-n quantum library in your research work, we would be grateful if you cited our publication:

A. Al-Bayaty, X. Song, and M. Perkowski, "CALA-n: A quantum library for realizing cost-effective 2-, 3-, 4-, and 5-bit gates on IBM quantum computers using Bloch sphere approach, Clifford+T gates, and layouts," 2024, arXiv:2408.01025.

Or, using BibTeX style:

@article{calaquantumlibrary,
    title={CALA-n: A quantum library for realizing cost-effective 2-, 3-, 4-, and 5-bit gates on IBM quantum computers using Bloch sphere approach, Clifford+T gates, and layouts},
    author={Ali Al-Bayaty, Xiaoyu Song, and Marek Perkowski},
    journal={arXiv preprint arXiv:2408.01025},
    year={2024},
    url={https://doi.org/10.48550/arXiv.2408.01025}
}

Name		Name	Last commit message	Last commit date
Latest commit History 60 Commits
.github/workflows		.github/workflows
images		images
src		src
tests		tests
.gitignore		.gitignore
CODE_OF_CONDUCT.md		CODE_OF_CONDUCT.md
LICENSE		LICENSE
README.md		README.md
pyproject.toml		pyproject.toml
requirements-dev.txt		requirements-dev.txt
requirements.txt		requirements.txt
setup.py		setup.py
tox.ini		tox.ini

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

Repository files navigation

CALA-n Quantum Library

Installation

Usage

Examples

Reference

About

Languages

License

albayaty/cala_quantum_library

Folders and files

Latest commit

History

Repository files navigation

CALA-n Quantum Library

Installation

Usage

Examples

Reference

About

Resources

License

Code of conduct

Stars

Watchers

Forks

Languages